MMME3087 - Department of Mechanical, Materials and Manufacturing Engineering

Assignment Task

Question

1 An infinite beam is supported on a rubber surface that can be considered as an elastic foundation. Elcharacterizes the stiffness of the beam, and the foundation has a stiffness of k (n/m2 ). An angle bracket is used to apply point load f at the location shown in Fig.

1. a. Using the theory of beams on an elastic foundation, derive expressions for the vertical deflection and slope of the beam (assuming that the angle bracket is a rigid component with a negligible deformation).

b. For a design analysis purpose, consider a beam made of aluminium (E= 70 GPa) with a depth of 100 mm, a width of 550 mm, L= 80 m, and a concentrated load F = 2 kn. Use ANSYS to address the following:

• Discuss the effect of increasing the length a from 0 to 1 m on the maximum deflection of the beam. Take it that the beam is under an elastic foundation with a stiffness 5 MPa.
• Discuss the effect of the number of elastic springs used to represent the elastic foundation on the deflection and bending stress of the beam.
• Discuss if it is possible to compare the theoretical solution obtained for the deflection and the slope in Q1(a) with the numerical solution from ANSYS for the case of a = 0.2m

2. The integrated pressure vessel and its support structure shown in Fig. 2(a) is to be designed to meet acceptable engineering criteria. Mostly, the pressure vessel is used in the storage of wet grain and its bottom experiences a 5 MPa pressure when it is fully loaded.

(a) Assuming the supporting structure can be idealized as a flat annular circular plate (see Fig. 2(b) and 2(c)), for which the equation of the vertical deflection (w) due to the applied surface pressure (p) is obtained as:

i. Recommend a material that can be used for the circular plate with appropriate justifications.

ii. Select a specific combination of the thickness of the plate (t), a and b. See Fig. 2(c) indicating the parameters a and b. Ensure that the geometric information you select satisfies the condition for the use of a thin-plate theory.

iii. Analyse the problem using ANSYS to verify the validity of the above equation using the values specified in the previous steps.

iv. Discuss the variation of the radial stress against the ratio b/a.

(b) The circular plate theory has wider applications in the design of many components. One such application relates to the design of pressure sensors. Conduct a literature review to summarize the design and operation of a diaphragm-based pressure sensor. Using the knowledge from the literature review, briefly discuss, in your own words, how the theory of circular plate is relevant in the design of diaphragm-based pressure sensors. The discussion should not exceed a single page.

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